200 hrs of Skilled Labour/Labor @ Rs. 20 per hr, 400 hrs of SemiSkilled Labour/Labor @ Rs. 15/hr and 150 hrs of Unskilled Labour/Labor @ Rs. 10 per hr were planned to be utlised for manufacturing 7,500 units of a product.
240 hrs of skilled labour/labor @ Rs. 22 per hr, 500 hrs of Semiskilled labour/labor @ Rs. 14/hr and 220 hrs of Unskilled labour/labor @ Rs. 12 per hr were actually used for manufacturing 7,125 units of the product.
16 hrs of Skilled Labour/Labor time, 50 hrs of SemiSkilled Labour/Labor time and 22 hrs of Unskilled Labour/Labor time were lost due to break down which is abnormal.
What is the variation in total cost on account of variation in the wage rates?
This information is provided by the Labour/Labor Rate of Pay variance.
The problem data arranged in a working table:

Standard [Production: 7,500 units] 
Actual [Production: 7,125 units] 
Time (hrs) 
Rate (Rs/hr)
 Cost (Rs) 
Rate (Rs/hr) 
Gross/Total 
Net 
Abnromal 
Time (hrs) 
Cost (Rs) 
Time (hrs) 
Cost (Rs) 
Time (hrs) 
Cost (Rs) 
Skilled 
200 
20 
4,000 
22 
240 
5,280 
216 
4,752 
24 
528 
Semi Skilled 
400 
15 
6,000 
14 
500 
7,000 
450 
6,300 
50 
700 
Un Skilled 
150 
10 
1,500 
12 
220 
2,640 
198 
2,376 
22 
264 
Total
 750 

11,500 

960 
14,920 
864 
13,428 
96 
1,492 
You need not calculate the data for SR_{Mix} and AR_{Mix} for the purpose of calculating Labour/Labor Rate of Pay Variance.

The Formulae » Labor/Labour Rate of Pay Variance (LRPV)



The variance in the total cost of labour/labor on account of a variation between the standard rate (rate at which the labourers/laborers should have been paid) and the actual rate (rate at which they have been paid).
It is calculated as the difference between the standard cost of actual labour/labor time and the actual cost of labour/labor.
⇒ Labour/Labor Rate of Pay Variance

= 
Standard Cost of Actual Labour/Labor Time − Actual Cost of Labour/Labor


= 
(Actual Time × Standard Rate) − (Actual Time × Actual Rate)

Memorise this general formula for easier recollection (ignoring the specific formulae below)
For each Labour/Labor Type Separately

For all Labour/Labor Types together [Total Labour/Labor Rate of Pay Price Variance :: TLRPV]
When two or more types of labour/labor are used for the manufacture of a product, the total Labour/Labor Rate of Pay variance is the sum of the variances measured for each labour/labor type separately.
No Direct Formula
There is no direct formula for calculating the total labour/labor rate of pay variance.
TLRPV ≠ AT_{Mix} (SR_{Mix} − AT_{Mix})

LRPV Formula interpretation



The above formulae for Labour/Labor Rate of Pay Variance can be used in all cases i.e. when AO = SO, AO ≠ SO, ST _{Mix} = AT _{Mix} and ST _{Mix} ≠ AT _{Mix}. Standard Rate present in the formula is unaffected by standard recalculation. Standard Time which changes on recalculating standards is not found in the formula.
Actual Time ⇒ Gross Time
Wherever you find the presence of time in the formula, you should interpret it as Actual (Gross) Time. Where there abnormal loss of time, the actual time is segregated into two as abnormal loss time and net time. Even in such cases, for the purpose of calculating the Cost Variance, the total (Gross) time should be considered for actual time.
LRPV = 0
Labouir/Labor Rate of Pay Variance for each labour/labor type be zero if the rate at which the labourers/laborers are paid i.e. actual rate (AR) is the same as its standard wage rate (SR).
TLRPV = 0
When more than one type of labour/labor is used, the Total Labour/Labor Rate of Pay Variance may become zero
 When the LRPV on account of each labour/labor type is zero, or
 When the unfavourable variance due to one or more labour/labor types is set off by the favourable variance due to one or more other labour/labor types.
Therefore, it would not be appropriate to conclude that all the labour/labor time is paid at the standard rates just because the total LRPV is zero.
Where the total LRPV is zero, you have to verify individual variances before concluding that all the individual variances (LRPV's) are zero.

Recalculating Standards does not effect LRPV Calculations



Recalculating Standards does not affect the data used for calculating Labour/Labor Rate of Pay Variance. The formula for calculating Labour/Labor Rate of Pay Variance involves AT, SR and AR. It does not involve and thus is not influenced by ST. These data would not change on standards being recalculated either based on the output or input.
SO ≠ AO and ST_{Mix} ≠ AT_{Mix}

Standard [Production: 7,500 units] 
Actual [Production: 7,125 units] 
Time (hrs) 
Rate (Rs/hr)
 Cost (Rs) 
Rate (Rs/hr) 
Total 
Normal 
Abnromal 
Time (hrs) 
Cost (Rs) 
Time (hrs) 
Cost (Rs) 
Time (hrs) 
Cost (Rs) 
Skilled 
200 
20 
4,000 
22 
240 
5,280 
216 
4,752 
24 
528 
Semi Skilled 
400 
15 
6,000 
14 
500 
7,000 
450 
6,300 
50 
700 
Un Skilled 
150 
10 
1,500 
12 
220 
2,640 
198 
2,376 
22 
264 
Total
 750 

11,500 

960 
14,920 
864 
13,428 
96 
1,492 
Standards Recalculated for the Actual Output

Standard [Production: 7,125 units] 
Actual [Production: 7,125 units] 
Time (hrs) 
Rate (Rs/hr)
 Cost (Rs) 
Rate (Rs/hr) 
Total 
Normal 
Abnromal 
Time (hrs) 
Cost (Rs) 
Time (hrs) 
Cost (Rs) 
Time (hrs) 
Cost (Rs) 
Skilled 
190 
20 
3,800 
22 
240 
5,280 
216 
4,752 
24 
528 
Semi Skilled 
380 
15 
5,700 
14 
500 
7,000 
450 
6,300 
50 
700 
Un Skilled 
142.5 
10 
1,425 
12 
220 
2,640 
198 
2,376 
22 
264 
Total
 712.5 

10,925 

960 
14,920 
864 
13,428 
96 
1,492 
Standards Recalculated for Actual Input

Standard [Production: 8,640 units] 
Actual [Production: 7,125 units] 
Time (hrs) 
Rate (Rs/hr)
 Cost (Rs) 
Rate (Rs/hr) 
Total 
Normal 
Abnromal 
Time (hrs) 
Cost (Rs) 
Time (hrs) 
Cost (Rs) 
Time (hrs) 
Cost (Rs) 
Skilled 
230.4 
20 
4,608 
22 
240 
5,280 
216 
4,752 
24 
528 
Semi Skilled 
460.8 
15 
6,912 
14 
500 
7,000 
450 
6,300 
50 
700 
Un Skilled 
172.80 
10 
1,728 
12 
220 
2,640 
198 
2,376 
22 
264 
Total
 864 

13,248 

960 
14,920 
864 
13,428 
96 
1,492 

The data that is used for calculating Labour/Labor Rate of Pay Variances can be picked up from the working table built with the data given (as it is) or with the data involving recalculated standards based on either the Actual Output or the Actual Input.
LRPV = (AT_{G} × SR) − (AT_{G} × AR) ⇒ LRPV = AT_{G} (SR − AR)
Using LRPV_{Lab} = AT_{(G)Lab} (SR_{Lab} − AR_{Lab})
Labour/Labor Rate of Pay Variance due to Workers who are
• Skilled 
= 
240 hrs (Rs. 20/hr − Rs. 22/hr) 

= 
240 hrs (− Rs. 2/hr) 

= 
− Rs. 480 
⇒ LRPV_{Sk} 
= 
− Rs. 480 [Adv] 
• SemiSkilled 
= 
500 hrs (Rs. 15/hr − Rs. 14/hr) 

= 
500 hrs (Rs. 1/hr) 

= 
+ Rs. 500 
⇒ LRPV_{Se} 
= 
+ Rs. 500 [Fav] 
• Unskilled 
= 
220 hrs (Rs. 10/hr − Rs. 12/hr) 

= 
220 hrs (− Rs. 2/hr) 

= 
− Rs. 440 
⇒ LRPV_{Un} 
= 
− Rs. 440 [Adv] 


Total Labour/Labor Rate of Pay Variance 
= 
− Rs. 420 [Adv] 

Formulae using Interrelationships among Variances



Who is held responsible for the Variance?



Since this variance is on account of the wage rate paid being more or less than the standard, the people or department responsible for deciding the wage rates actually to be paid can be held responsible for this variance.


